In crowding, target perception deteriorates in the presence of flanking elements. Crowding is classically explained by low-level mechanisms such as pooling or feature substitution. However, we have previously shown that perceptual grouping between the target and flankers, rather than low-level mechanisms, determines crowding. There are many grouping cues that can determine crowding, such as low- and high-level feature similarity, low- and high-level pattern regularity, and good Gestalt. Here we show that pattern completion, another grouping cue that is important for crowding in foveal vision, is also important in peripheral vision. We also describe computer simulations that show how pattern completion, and crowding in general, can be partly explained by recurrent processing.